Abstract
The authors study thermally activated hopping processes on regularly multifurcating ultrametric spaces (UMS) and investigate the first two moments of the range Rn, where n is the number of steps. Paralleling the recent findings for Cayley trees, the knowledge of exact generating functions for these moments permits to draw conclusions about their behaviour for large n. For the first moment, the mean number of distinct sites visited, Sn, they derive analytically the cross-over from a linear behaviour in the transient regime gamma )1 to a sublinear increase Sn approximately ngamma in the recurrent regime gamma (1. Here as usual for UMS, the parameter gamma depends linearly on the temperature. The second moment of Rn, the variance vn, displays different behaviour corresponding to strongly transient ( gamma >2), not strongly transient (1( gamma (2) and recurrent ( gamma (1) random walks. All results are verified by comparison to computer data obtained through simulations and through numerical series expansions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.